From the looks of it, it is probably Cyano or red slime algae. It does and can spread and if the conditions are right very rapidly at that.
This type of algae is usually caused by excess phosphates/ or excess nitrates or a combination of the two. These can be caused by a number of things, but in my experience there are usually two main causes.
#1 high nitrate levels caused by over feeding
#2 high phosphate levels by adding salts that are not phosphate free, or adding water which contains phosphates.
Solutions, do not feed as much, maybe every other day (Yes your fish will be fine) also try and do more frequent water changes, as for phosphates try and use RO/DI water. Rather than tap, if you are not using tap water contact the source of the water that you are using and ask them about there filtering method.
If you are using RO/DI water ask them when the last time they changed there filters were.
This should help.